Internal Rotation Rate Research Articles

Inversion methods in helioseismology and solar tomography

Basic methods by which the internal structure and dynamics of the Sun can be inferred from observed frequencies of solar oscillations and acoustic travel times are discussed. The methods for inverting the oscillation frequencies are based on a variational formulation of the adiabatic eigenvalue problem for a star. The inversion technique formulated in terms of linear integral constraints provides estimates of localized averages of properties of the solar structure, such as density and sound speed, helium abundance in the convection zone for a given equation of state, and, in addition, the estimates for the internal rotation rate. The method of inverting acoustic travel times employs a geometrical ray approximation and provides 3D images of solar convective cells, active regions and sunspots. The information about the global and local structures and flow velocities in the solar interior is important for understanding solar evolution and mechanisms of solar activity. The high-resolution helioseismology projects from space provide a tremendous amount of data, the interpretation of which is increasingly challenging and requires the development of efficient inversion methods and algorithms.

Characteristics of the Galileo probe entry site from Earth‐based remote sensing observations

A reassessment of ground‐based observations confirms to better than a 98% confidence level that the Galileo probe entered a 5‐μm hot spot, a region of unusual clarity and dryness, some 900±300 km north of its southern boundary. Cloud conditions at that point were similar to those in the center of this region, some 600 km further north. At the time of the probe entry, the region was evolving to a slightly larger size and even thinner cloud conditions, as evidenced by its rapidly brightening appearance at 4.78 μm. The low reflectivity of the region in red light is highly anticorrelated with 4.78‐μm thermal emission, but this correlation breaks down in the blue. In general, the reflectivity of most hot spots is remarkably uniform, although the 4.78‐μm thermal emission is highly variable. A cloud structure most consistent with both the observed reflected sunlight and thermal emission properties consists of two layers: (1) a cloud layer above the 450‐mbar level extending up to the 150‐mbar level that probably consists of submicron sized particles and (2) a tropospheric cloud that is probably below the 1‐bar level, possibly ammonia hydrosulfide, with low optical thickness in the infrared. A population of particles larger than ∼3 μm, clearly present at the NH3 ice cloud level outside hot spots, is absent inside them. The NH3 gas abundance near 300–400 mbar pressure does not appear to be unusually depleted in hot spots. Zonal structures in the tropospheric temperature field near the probe entry site were not correlated with the location of 5‐μm hot spots but moved at speeds closer to the internal rotation rate of the planet. The properties of the tropospheric thermal waves at the probe entry latitude show little correlation to the properties of the 5‐μm hot spot waves. Temperatures at the probe entry site derived from remote sensing are warmer than the Atmospheric Structure Instrument (ASI) experiment results near the tropopause, probably because the low‐temperature ASI features are confined to regions smaller than the ∼6000‐km resolution characteristic of the remote sensing.

The Internal Solar Rotation Rate Inferred from Combined GONG and LOWL Data

Frequency splittings derived from the first 4 months of GONG data and from the 2 yr average of the LOWL data in the form of the Clebsch-Gordon coefficients are analyzed. The results show that the equatorial rotation rate is essentially flat (i.e., independent of radius) for 0.2 < R/R☉ < 0.6. They also indicate an increase in the rotation rate at high latitudes (of ~15% at latitude 60° for R/R☉ < 0.4), but it is emphasized that this result is a property of the data sets and should not be regarded as a property of the Sun without independent confirmation.

The Internal Rotation Rate Inferred from Lowl and Gong Data: Using a Forward Method

Recently the LOWL Group has made available 2-year averages of frequency splitting data obtained mainly for low values of the degree ℓ. Charbonneau et al. (1997) find a nearly flat rotational curve in the deep radiative core from these data using a Genetic Forward Modeling method. Subsequently, they test the assumption of latitude independence for r &lt; 0.5 by performing a 1.5-D inversion, and find a rotation rate which is 25% greater at the pole than at the equator for 0.1 &lt; r &lt; 0.2.

Kinetics of Internal Rotation of N,N-Dimethylacetamide: A Spin-Saturation Transfer Experiment

A new experiment for the undergraduate physical chemistry laboratory is presented for the application of dynamic nuclear magnetic resonance (DNMR) spectroscopy to the study of internal rotation kinetics in N, N-dimethylacetamide (DMA). Spin-lattic relaxation times (T1) were measured by the inversion recovery method and rates of internal rotation about the amide bond in DMA were measured bya spin-saturation transfer method in the temperature range 5-23°C. The activation parameters, DeltaH298 = 70.6+1.4 kJ/mol and DeltaS298 = -11+5 kJ/mol, were determined from the temperature dependence of the rate of internal rotation. Through the temperature range used in the present work is quite narrow compared with the line-shape analysis experiment, the derived thermodynamic data are in excellent agreement with more extensive measurements.

NMR Study of Pressure Effect on the Hindered Rotation in cis-1,12-Disubstituted[12]paracyclophanes

Abstract Effect of hydrostatic pressure on the rate of internal rotation of title compounds has been examined by DNMR method. A quartz high–pressure NMR cell was used to realize the high–pressure experiment up to 300 MPa. The rate of internal rotation, lnk was found to increase linearly up to 300 MPa.

NMR Determination of Internal Rotation Rates and Rotational Energy Barriers: A Physical Chemistry Lab Project

This article describes an experiment suitable for Physical Chemistry laboratories. It consists of an improved method to analyze the kinetics of internal rotation around the C-N amidic bond. The improvement over traditional experiments relies on the use of a saturation transfer NMR technique which allows the expansion of the typically narrow temperature range available in conventional NMR lineshape analysis experiments with dimethylacetamide.This experiment will expose students to a variety of NMR techniques, such as saturation transfer, inversion-recovery, and lineshape analysis. It will also demonstrate that NMR is an extremely useful tool to chemists, with very relevant applications in physical chemistry.

Theory and application of fully anisotropic overall molecular tumbling, with restricted group internal rotation: 13C NMR relaxation studies of sodium taurocholate and ginsenoside‐Re

AbstractA theory is presented for fully anisotropic overall molecular tumbling with restricted group internal rotation. This formalism is used with 13C NMR relaxation data and results from molecular mechanics to compute the rotational diffusion rates and methyl group internal rotation rates for sodium taurocholate and ginsenoside‐Re in organic solvents. Although existing theories for steroid derivatives describe methyl internal rotation in terms of free isotropic motion, methyl rotation in ginsenoside‐Re is found to be both sluggish and spatially restricted. The energetic barrier to methyl internal rotation increases significantly with the bulkiness of flexible side‐chains in a series of steroid natural products.

Structure and dynamics of a series of crystals of butterfly-like molecules as studied by 35Cl NQR, and 1H and 19F NMR

4,4′-Difluorobenzophenone (DFBP), 2,2-bis(4-chlorophenyl)-1,1-dichloroethylene and dichlorodiphenylmethane have been investigated by 35Cl nuclear quadrupole resonance, and 1H and 19F nuclear magnetic resonance. The spin-lattice relaxation times T 1 of 1H and 19F of DFBP assume minima at about 60 K, suggesting that the internal rotation of the C 6H 5F group is excited at low temperatures. The T 1 of 1H changes drastically at the first-order phase transition point (≈ 100 K), due probably to the abrupt change in the rate of internal rotation of the C 6H 5F group. The asymmetric temperature curve of T 1 indiates that the stochastic internal rotation cannot be described by a single correlation time of the motion. 35Cl NQR reveals that 2,2-bis(4-chlorophenyl)-1,1-dichloroethylene and dichlorodiphenylmethane do not exhibit any phase transition between 4.2 K and their respective melting points.

Reverberation mapping of active galactic nuclei: The SOLA method for time-series inversion

In this paper a new method is presented to find the transfer function of the broad-line region in active galactic nuclei. The subtractive optimally localized averages (SOLA) method is a modified version of the Backus-Gilbert method and is presented as an alternative to the more often used maximum-entropy method. The SOLA method has been developed for use in helioseismology. It has been applied to the solar oscillation frequency splitting data currently available to deduce the internal rotation rate of the sun. The original SOLA method is reformulated in the present paper to cope with the slightly different problem of inverting time series. We use simulations to test the viability of the method and apply the SOLA method to the real data of the Seyfert-1 galaxy NGC 5548. We investigate the effects of measurement errors and how the resolution of the TF critically depends upon both the sampling rate and the photometric accuracy of the data. A uuencoded compressed postscript file of the paper which includes the figures is available by anonymous ftp at ftp://solaris.astro.uu.se/pub/articles/atmos/frank/PijWan.uue

Storage of Magnetic Flux in the Overshoot Region

The combined action of the subadiabatic ambient stratification in the overshoot region below the convection zone and the inertial forces associated with the solar rotation is shown to lead to the suppression of the escape of magnetic flux in the form of toroidal flux tubes both toward the surface and toward higher latitudes. We show that a flux ring initially in thermal equilibrium with its environment and rotating with the ambient angular velocity moves radially and latitudinally towards an equilibrium configuration of lower internal temperature and larger internal rotation rate with respect to the surrounding, field-free gas. We conclude that flux rings with B≲ 105 G can be kept within the overshoot region if the superadiabaticity is sufficiently negative, i.e. δ = ▿ – ▿ad≲–10−5; below that field strength the poleward drift is also reduced to a latitudinal oscillation of moderate amplitude, δθ ≲ 20 deg. Flux rings with significantly larger field strength cannot be kept in the equatorial parts of the overshoot region: their equilibrium configuration is located at high latitudes far outside the solar activity belts and, at any rate, requires unrealistic values of δ.

The resolving power of current helioseismic inversions for the sun's internal rotation

The inferred internal solar rotation rate obtained from helioseismic inversion is a nonlocal average of the true rotation rate; hence some care is required in the interpretation of the results of such inversions. We present kernels which describe the weighting of the average, for an inversion that is representative of recent work. Of particular interest is the fact that the so-called polar rate is actually an extrapolation from lower latitudes: the current helioseismic data do not permit us to construct a solution whose averaging kernel is localized at high solar latitude

Selective excitation of deuterium powder patterns for studies of molecular motion in solids

The rate of internal rotation of the amino group in solid p-nitroaniline-N,N-d{sub 2} has been determined from NMR hole-burning experiments. This work represents the first use of quantitative simulations of selectively perturbed deuterium powder patterns and the results demonstrate the potential of this technique for characterization of molecular motion in solids.

Reorientational dynmics and internal rotation in W(PMe 3)(CO) 5

Oxygen-17 and methyl group carbon-13 NMR spin-lattice (T 1) relaxation times were measured in the metal carbonyl, W(PMe 3)(CO) 5, as a function of temperature in the solvent chloroform. Perpendicular and parallel rotational diffusion coefficients (D 1 and D d), calculated from T 1( 17O) of the axial and radial carbonyls were compared with the predictions of various a priori theories of molecular reorientation. The Nu-Zwanzig ‘slip’ model yielded values more than an order of magnitude greater than experiment. Calculated diffusion constants from the Perrin ‘stick’ theory and the newer Hynes-Kapral-Weinberg model were approximately a factor of three times smaller or greater, respectively, than the measured values. Rotational correlation times, τ c(CH), were calculated from methyl 13C relaxation times and nuclear Overhauser enhancements. These values were used, together with the rotational barrier in free trimethylphosphine, to calculate the rates of internal rotation about the PW and PC bonds. It was observed that there is a significant degree of rotation about both of these bonds in W(PMe 3)(CO) 5. However, in neither case were the rates as rapid as would be expected in the absence of a barrier to internal rotation.

The latitude belts of solar activity as a consequence of a boundary-layer dynamo

HELIOSEISMOLOGY has provided much insight into the Sun's activity, allowing measurements of the thickness of the solar convection zone and the internal solar rotation rate as a function of latitude and depth. Solar activity is generally thought to result from dynamo action within the Sun, but there has been some debate as to whether this action occurs in the whole convection zone, at the base of the convection zone, or in the boundary layer between the convection and radiative zones1,2 (about 0.65 R⊙ to 0.7 R⊙). Here we point out that recent helioseismological data3–7 seem consistent with the last location. We present the results of calculations on a model in which dynamo action arises in a very thin (0.05 R⊙) spherical boundary layer, which are consistent with the observations. In particular, this model provides an explanation of why there exists a latitudinal boundary on the solar surface, below which features such as sunspots migrate towards the equator whereas above it they migrate polewards.

Enzyme-inhibitor complexes of lysozyme with glucosamine inhibitors A molecular dynamics study through 2H-NMR

2H relaxation measurements coupled with multiple specific 2H labeling have provided insight into the molecular dynamics of N-acetyl-D-glucosamine (GlcNAc) inhibitors bound to lysozyme. Deuteron T1 and T2 data for the bound state of methyl alpha- and -beta-GlcNAc 2H-labeled in the glycosidic methyl and C2 positions have been derived from measurements at different enzyme/inhibitor ratios. Rotational correlation times calculated therefrom for the labeled sites indicate, in both cases, tight binding for the sugar ring (tau(b) = 3.0 x 10(-9) s) accompanied by fast internal rotation, about one axis, of the glycosidic methyl groups (tau(r) = 5.5-7.6 x 10(-11) s). The small but consistent difference in the rates of internal rotation for the alpha- and beta-anomeric inhibitors may be indicative of different solution structures of the enzyme-inhibitor complexes.

Reorientational dynamics and the barrier to internal rotation in Cp2Co3(.mu.2-CO)(CO)3(.mu.3-CPh)

NMR spin-lattice relaxation times of the phenyl, cyclopentadienyl, and terminal carbonyl 13 C nuclei in the title compound were measured as a function of temperature in the solvent chloroform. The phenyl carbon T 1 's were used to calculate the diffusion coefficient characterizing the ring's net spinning rate. Internal rotation rates of the cyclopentadienyl groups, R(Cp), were found to be far greater than R(Ph) at all temperatures, indicating that the barrier to phenyl group rotation is not due to inter-ring steric repulsions. Rather, it can be attributed to an electronic interaction of the bridging carbonyl's π* orbital with the phenyl π system through the metal 2e and carbynyl 2p orbitals. This is only the second system in which a bridging carbonyl/capping group orbital interaction has been observed and the first for which the barrier range to internal rotation has been experimentally determined

What we know about the sun's internal rotation from solar oscillations

In this paper, a uniform approach of inversion was used to determine the internal rotation rate of the sun from each of the six available sets of solar oscillation data, which included the data of Duvall et al. (1986), Rhodes et al. (1987, 1990), Tomczyk (1988), Brown and Morrow (1987), and Libbrecht (1989). The technique chosen for inverting the solar oscillation data was the discretized least-squares technique. The results indicate that the rotation rate of the sun in the equatorial plane declines going inward between the surface and 0.6 of the radius and that the polar rate increases going inward (i.e., the surfacelike differential rotation decreases with depth).

Solar-cycle dependence of the Sun's deep internal rotation shown by helioseismology

HELIOSEISMOLOGY, the study of solar oscillations, yields information on the Sun's internal rotation and magnetism which is of great importance in understanding the 22-year solar cycle. We show here that helioseismic data suggest that the Sun's internal rotation rate, at depths greater than half the solar radius, has changed systematically during the most recent cycle. There is no variation, however, in the rotation over a range of intermediate solar radii covering the upper part of the Sun's radiative interior and the lower part of the convective zone; this intermediate region is where, according to the same helioseismic data, an abrupt change in rotation rate with depth accompanies the transition from convective to radiative structure. We suggest that the modulation of the rotation rate in the Sun's interior could be caused by a torsional oscillation, provided that a poloidal magnetic field of kilogauss strength exists in the radiative interior.

Prisma-probing rotation and interior of stars: Microvariability and activity

The measurement of frequencies, amplitudes and lifetimes of solar oscillations has proven to be a very powerful tool to sound the properties of the solar internal structure. Combined with observations of emerging solar magnetic field parameters of the solar internal structure and dynamo can be inferred. The same techniques may be used to sound stellar interiors: asteroseismology and observation of magnetic activity (emerging magnetic fields). The observation of photometric fluctuations down to micromagnitudes on stars along or near the main sequence when complemented with measurements of activity levels will provide a wealth of information on the internal structure and rotation rates, and its evolutions with age. The PRISMA mission is an ESA Assessment Study currently underway. We present here the scientific objectives of the mission, the measurements to be made, the techniques to be used, and the main characteristics of a model payload.